The current price of a non$-$dividend$-$paying stock is $$63\mathrm{.}12$ and you expect the stock price to either go up by a factor of $1\mathrm{.}446$ or down by a factor of $0\mathrm{.}713$ each period for $2$ periods over the next $1$ years. Each period is $0\mathrm{.}5$ years long.

A European call option on the stock expires in $1$ years. Its strike price is $$63.$ The risk$-$free rate is $3\%($annual$,$ continuously compounded$).$ What is the current value of the option?